Broadband surface-wave transformation cloakSu Xua,b,1, Hongyi Xuc,d,1, Hanhong Gaoe, Yuyu Jianga,b, Faxin Yuf, John D. Joannopoulosg,2, Marin Soljaci�cg,Hongsheng Chena,b,g,2, Handong Sunc,d,2, and Baile Zhangc,d,2

aState Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China; bThe Electromagnetics Academy at ZhejiangUniversity, Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China; cDivision of Physics and AppliedPhysics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371; dCentre for Disruptive Photonic Technologies,Nanyang Technological University, Singapore 637371; eDepartment of Electrical Engineering and Computer Science, Massachusetts Institute of Technology,Cambridge, MA 02139; fSchool of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China; and gResearch Laboratory of Electronics,Massachusetts Institute of Technology, Cambridge, MA 02139

Contributed by John D. Joannopoulos, May 7, 2015 (sent for review February 27, 2015; reviewed by Demetrios Christodoulides and Michelle L. Povinelli)

Guiding surface electromagnetic waves around disorder withoutdisturbing the wave amplitude or phase is in great demand formodern photonic and plasmonic devices, but is fundamentally dif-ficult to realize because light momentum must be conserved in ascattering event. A partial realization has been achieved byexploiting topological electromagnetic surface states, but this ap-proach is limited to narrow-band light transmission and subject tophase disturbances in the presence of disorder. Recent advancesin transformation optics apply principles of general relativity tocurve the space for light, allowing one to match the momentumand phase of light around any disorder as if that disorder were notthere. This feature has been exploited in the development of in-visibility cloaks. An ideal invisibility cloak, however, would requirethe phase velocity of light being guided around the cloaked objectto exceed the vacuum speed of light—a feat potentially achievableonly over an extremely narrow band. In this work, we theoreti-cally and experimentally show that the bottlenecks encountered inprevious studies can be overcome. We introduce a class of cloakscapable of remarkable broadband surface electromagnetic wavesguidance around ultrasharp corners and bumps with no percepti-ble changes in amplitude and phase. These cloaks consist of spe-cifically designed nonmagnetic metamaterials and achieve nearlyideal transmission efficiency over a broadband frequency rangefrom 0+ to 6 GHz. This work provides strong support for the ap-plication of transformation optics to plasmonic circuits and couldpave the way toward high-performance, large-scale integratedphotonic circuits.

transformation optics | surface wave | invisibility cloaks | broadband

One of the main limitations in plasmonic circuitry and devices(1, 2) that use surface electromagnetic waves (surface plas-

mons at optical frequencies) as information and energy carriers isthe inability to perfectly guide surface electromagnetic wavesaround unavoidable disorders, such as sharp corners. Althoughnear-perfect transmission around sharp corners in electronic cir-cuits is routine, it is fundamentally difficult to realize with surfacewaves, because surface waves suffer from scattering loss whenencountering sharp corners or other irregular disorders.Scattering-free guidance of surface waves around sharp corners

has been shown only in topological electromagnetic surface states(3–7). It has been developed in analogy with electronic chiral edgestates in quantum Hall systems (8) and topological insulators (9,10). To force the waves to circumvent disorders, the studies citedabove typically require the use of photonic crystals with substantialmagnetic responses (11). The use of magnetic metamaterials limitsthese realizations to a narrow-microwave frequency band. The useof conventional nonmagnetic photonic materials, however, couldallow for scalability to the optical regime with broad bandwidth.The difficulty in sharp bending is the dramatic momentum mis-

match of surface electromagnetic waves before and after passing thesharp corner in an extremely compact space. Transformation optics(12, 13) allow for the design of inhomogeneous metamaterials thatcontrol light by effectively warping the electromagnetic space

analogously to the way that gravity curves space in general relativity.Because the concept of momentum stems essentially from spacehomogeneity (14), an effectively curved electromagnetic spaceprovides a method to match wave momenta by compensating forthe asymmetry of spatial translation around sharp corners. Surfaceelectromagnetic waves can be, thereby, deceived that they are stillpropagating along a flat surface without any corners.In the past few years, transformation optics has been used to

develop invisibility cloaks to hide objects from free-space propa-gating electromagnetic waves (15–23). An ideal invisibility cloak is afundamentally narrow band, because it would require the phasevelocity of light being guided around the “cloaked object” to exceedthe vacuum speed of light (13, 15, 24). However, surface elec-tromagnetic waves are essentially slow waves, with bending thatwill not cause superluminal propagation in the majority of situa-tions, but all of the potential applications of transformation opticsin surface electromagnetic waves (25–29) so far are still theoreti-cal. Most theoretical designs only deal with objects with relativelysmooth surfaces or finite bending radii (25, 26). Refs. 28 and 29proposed alternative surface wave-bending approaches; however,in general, scattering will occur when an ultrasharp bending withzero radius is desired. Therefore, if a similar approach of sharpbending could be realized for surface waves, many unique con-ceivable applications would become feasible: not only waveguidesfor sharp right-angle corners (3) but also, carpet cloaks that canhide irregular bumps on the metal–dielectric interface (26), superplasmonic resonators with extremely high Q values (30), etc.Here, we present experimental demonstration of broadband

sharp bending of surface electromagnetic waves with almost

Significance

Guiding surface electromagnetic waves around disorder with-out disturbing the wave amplitude or phase is in great demandfor modern photonic and plasmonic devices. In this work, weintroduce a class of cloaks capable of remarkable broadbandsurface electromagnetic waves guidance around ultrasharpcorners and bumps with no perceptible changes in ampli-tude and phase. This work provides strong support for theapplication of transformation optics to plasmonic circuits andcould pave the way for high-performance, large-scale in-tegrated photonic circuits.

Author contributions: S.X., H.X., H.C., and B.Z. designed research; S.X., H.X., Y.J., and F.Y.performed research; H.G. contributed new reagents/analytic tools; S.X., H.X., J.D.J., M.S.,H.C., H.S., and B.Z. analyzed data; S.X., H.X., J.D.J., M.S., H.C., H.S., and B.Z. wrote thepaper; B.Z. conceived the study; and H.C., H.S., and B.Z. supervised the project.

Reviewers: D.C., College of Optics and Photonics, University of Central Florida; and M.L.P.,University of Southern California.

The authors declare no conflict of interest.1S.X. and H.X. contributed equally to this work.2To whom correspondence may be addressed. Email: joannop@mit.edu, hansomchen@zju.edu.cn, hdsun@ntu.edu.sg, or blzhang@ntu.edu.sg.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1508777112/-/DCSupplemental.

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ideal transmission, which allows “invisibility cloaking” of disor-ders, such as ultrasharp corners and bumps for surface electro-magnetic waves. The remarkable broadband guidance, lackingin previous scattering-free topological electromagnetic surfacestates and free-space invisibility cloaks, is because of two reasons.First, the slow-wave property of surface electromagnetic wavescan overcome the bottleneck of free-space invisibility cloaks,because its phase velocity does not need to exceed the vacuumspeed of light. Second, we adopt a fully nonmagnetic design withnaturally accessible dielectric parameters, whereas magnetic re-sponses were necessary to open the topological band gap fortopological electromagnetic surface states.We start with the demonstration of bending a surface elec-

tromagnetic wave across sharp right-angle corners at microwavefrequencies—similar to the previous demonstration of bending aguided topological surface electromagnetic wave in a photoniccrystal (3). We call the bending adaptor a “corner cloak,” becauseit effectively hides a corner to the wave as if the corner did notexist. Because metals at microwave frequencies are perfect electricconductors that generally do not support surface electromagneticwaves, here we adopt the approach of geometrically induced orspoof surface plasmons (31) [i.e., we use a grooved metallic surface(referred to as a patterned metal in Figs. 1–3) to support surfaceelectromagnetic waves in the microwave regime]. Fig. 1A shows theexperimental setup: a U-shaped surface-wave waveguide (a metalbase with periodic grooves on its surfaces; i.e., the patterned metal)with two right-angle zero-radius corners. Given the sizes of thecloaks, the more confined the surface waves on the dielectric–metalinterface, the better the cloaking performance. To enhance theconfinement, we load the grooves with ceramic material withpermittivity «ceramic = 21. We use glass with permittivity «b = 4.6 asthe surrounding background that is to be impedance-matched withthe cloaks. More details can be found in Fig. S1 and SI Methods.The two identical corner cloaks locate at the two corners. This

structure that consists of the U-shaped waveguide and two cor-ner cloaks can be thought of as if it were transformed from astraight waveguide without any corner. A corner cloak, whentransformed back, corresponds to a triangular space on top ofthe dielectric–metal interface, which has an area that is pur-posely chosen to be the same as the corner cloak. This areapreservation guarantees nonmagnetism in the cloak design forsurface electromagnetic waves (more details are in Fig. S2 and SIMethods). The two identical corner cloaks require anisotropicconstitutive parameters. For each cloak, the required principalpermittivities in two orthogonal directions, «1 and «2, after theprocedure of diagonalization, where only components in the xyplane are relevant, are «1 = 10.7 and «2 = 2.0. These cloakswere implemented with a metamaterial consisting of a stackof the following two materials with subwavelength thicknesses:a microwave dielectric ceramic with permittivity «ceramic = 21(Wuxichaoying K-21; loss tangent:   1× 10−4; 1-mm thickness)and a polymer foam with permittivity «foam = 1.1 (Rohacell71HF; loss tangent:  16× 10−4; 1.06-mm thickness). According tothe standard formulas of effective medium theory, one can get

8<:

«1 = r«ceramic + ð1− rÞ«foam«2 = «ceramic«foam�ð1− rÞ«ceramic + r«foam

� ,

where the filling factor is given by r= 0.485. Fig. 1B shows thesimulation of the transmission of surface electromagnetic waveswhen the corners are not cloaked by the corner cloaks; a dra-matic scattering loss is evident. However, the transmission ofsurface electromagnetic waves across a sharp corner is perfectwhen both corners are cloaked by corner cloaks (Fig. 1C).A fabricated model with two corner cloaks is shown in Fig. 1D.

For comparison, we also fabricated a straight waveguide with

similar grooves and the same total propagation distance. Thetransmission data measured on the U-shaped surface-wave wave-guide from 0+ (100 MHz) to 6 GHz without/with corner cloaks arenormalized to the transmission data measured on the straightwaveguide (Fig. 1E). Without corner cloaks, the transmissionmeasured at the output of the U-shaped waveguide is close to zero,but when both sharp corners are hidden by the corner cloaks, thetransmission is almost unity. The experimental result shows near-perfect cloaking of two right-angle zero-radius corners for surfaceelectromagnetic waves in a broad bandwidth from 0+ to 6 GHz(i.e., with a fractional bandwidth of 200%).Next, we show a surface-wave carpet cloak used to cover an

ultrasharp bump on a flat metal–dielectric interface. Fig. 2A showsour experimental setup. Like in the realization of the cornercloaks, we used a metal base with grooves to support surfaceelectromagnetic waves. A sharp bump on the flat surface acts as anobstacle able to block the propagation of surface electromagneticwaves. The carpet cloak that can hide this sharp bump wasdesigned with a similar transformation optics approach (moredetails can be found in Fig. S3 and SI Methods). The numericalsimulation for the real structure in the presence of a sharp bump isshown in Fig. 2 B and C: without a carpet cloak, most of the waveenergy is scattered into the background medium near the apex ofthe bump; when the carpet cloak is put on top of the bump,however, the electromagnetic surface waves can be smoothly guidedaround the bump and returned to their original path as if the bumpwas not there. A fabricated model with a carpet cloak implementedwith the same metamaterial used in the corner cloaks is shownin Fig. 2D. The measured transmissions, normalized to the

Fig. 1. Surface-wave bending around sharp corners. (A) A U-shaped sur-face-wave waveguide with grooves on its surface covered by glass is illu-minated by a dipole antenna. The two sharp corners are covered by twocorner cloaks (i.e., layered structures with subwavelength foam and ceramicmaterials). A second dipole antenna located at the output of the waveguidemeasures the transmission. (B) Simulation of a surface wave when it en-counters a sharp corner that is not covered by a cloak. (C) Simulation of asurface wave when the sharp corner is cloaked by a corner cloak. (D) Photoof a fabricated model. The transmitter is shielded by the microwave ab-sorber material. (E) Measured normalized transmission of surface wavesthrough the waveguide. Exp., experimental data; Sim., simulation data.

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transmission through a straight waveguide without the bump,are shown in Fig. 2E. For the setup without a cloak, the nor-malized transmission is close to zero, indicating that the propa-gation of surface electromagnetic waves has been blocked by thebump. For the case with a carpet cloak, the normalized trans-mission approaches unity, showing near-perfect cloaking of asharp bump for surface electromagnetic waves in a broad band-width from 0+ to 6 GHz.

A striking feature, absent in topological electromagneticsurface states, is that, when the surface waves are perfectlyguided by the cloaks, the phase is preserved. We used a pulsedsignal to show this behavior. Fig. 3 shows the dynamic prop-agation of a pulse through the cloaks, which was obtained withthe commercial software COMSOL Multiphysics. A pointsource at port 1 excites a Gaussian-shaped pulse (bandwidth:0+–6 GHz; center frequency: 3 GHz) at 0 ns. The magnetic

Fig. 2. Surface-wave carpet cloaking. (A) A straight surface-wave waveguide with a sharp bump is illuminated by a dipole antenna. The surface of the metalbase is grooved similarly as that in Fig. 1A. The sharp bump is covered by a carpet cloak (i.e., a layered structure with subwavelength foam and ceramicmaterials). A second dipole antenna located at the output of the waveguide measures the transmission. (B) Simulation of a surface wave when it encountersthe sharp bump without a carpet cloak. (C) Simulation of a surface wave when the sharp bump is cloaked by the carpet cloak. (D) Photo of a fabricated model.The transmitter is shielded by the microwave absorber material. (E) Measured normalized transmission of surface waves through the waveguide. Exp., ex-perimental data; Sim., simulation data.

Fig. 3. A Gaussian-shaped pulse propagates on the patterned metal. A point source (port 1) generates the pulse at 0 ns. The bandwidth of the pulse is 6 GHz,and the center frequency is 3 GHz. The magnetic field distributions for three cases [(A) the corner cloaks, (B) the carpet cloak, and (C) the straight waveguidereference] are plotted to show the propagation of the pulse at five equivalent temporal sampling points.

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field distributions are plotted to show the propagation of thepulse on the patterned metal for the setup with the cornercloaks (Fig. 3A), the carpet cloak (Fig. 3B), and a straightwaveguide as a reference (Fig. 3C). For the realization withcorner cloaks, the signal reaches the first and second sharpcorners at 1.88 and 3.56 ns, respectively. At both sharp corners,the pulse signal is perfectly guided by the corner cloak, and atlast, it leaves the patterned metal from port 2. In the case ofthe carpet cloak, the pulse reaches the bump at 2.68 ns, and itis guided smoothly across the bump by the carpet cloak withoutany loss. The pulse reaches the same positions as in the straightwaveguide, with no relative delay, indicating that the phase iswell-preserved in a broad bandwidth by the cloaks. Movies S1and S2 show more details of the propagating pulse. Fig. 4shows the measured phase for the corner cloak (Fig. 4A) andcarpet cloak (Fig. 4B). The curves almost coincide with theirreferences over the frequency band from 0+ to 6 GHz, con-firming that the phase of the surface wave is well-preserved bythe cloaks.The above results show scattering-free guidance of surface

electromagnetic waves around large disorders, with both waveenergy and phase undisturbed in a 200% broad-frequency band.

Switching from free-space electromagnetic waves to surfaceelectromagnetic waves, transformation cloaks can find im-mediate applications without any fundamental limitations. Thefully nonmagnetic design makes it feasible to further extend tohigher frequencies and/or conventional surface waves. Our work,thereby, paves the way for the next generation of photonic andplasmonic devices, allowing for flexible design without concernin disorders.

ACKNOWLEDGMENTS. We thank P. Rebusco for critical reading and editingof the manuscript and Y. Deng for fabricating the samples. This work wassponsored by National Nature Science Foundation of China Grants 61322501and 61275183, the National Top-Notch Young Professionals Program, GrantFANEDDC-200950, the Program for New Century Excellent Talents (NCET-12-0489) in University, the Fundamental Research Funds for the CentralUniversities Grant FRFCU-2014XZZX003-24, a Nanyang Assistant Professor-ship Start-Up Grant, and Singapore Ministry of Education Grants Tier 1 RG27/12 and MOE2011-T3-1-005. The work at Massachusetts Institute of Tech-nology was supported by the US Army Research Laboratory and the USArmy Research Office through Institute for Soldier NanotechnologiesContract W911NF-13-D-0001, and M.S. was supported, in part, byMassachusetts Institute of Technology Solid State Solar Thermal EnergyConversion Energy Frontier Research Centers of Department of Energy Grantde-sc0001299.

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